Problem 17 - Chemistry for Allied Health

Question

What is the concentration, in units of ppm, for a solution that contains \(34 \mathrm{~g}\) of iron in \(365 \mathrm{~mL}\) of water?

Step-by-Step Solution

Answer

93150 ppm

Step 1: Convert Volume to Liters

First, convert the volume from milliliters to liters because ppm typically uses mass per unit volume in liters. Therefore, 365 mL is equivalent to 0.365 L since 1 L = 1000 mL.

Step 2: Calculate Mass per Liter

Determine how many grams of iron are dissolved per liter of solution. This is done by dividing the mass by the volume in liters: \[ \text{Mass per liter} = \frac{34 \text{ g}}{0.365 \text{ L}} \approx 93.15 \text{ g/L} \]

Step 3: Convert g/L to ppm

To convert grams per liter to parts per million (ppm), remember that 1 g/L is equal to 1000 ppm. Thus, \[ 93.15 \text{ g/L} = 93.15 \times 1000 \text{ ppm} = 93150 \text{ ppm} \]

Key Concepts

Understanding Parts Per Million (ppm)

When we talk about solution concentrations, particularly those involving very small amounts of solute, we often use the unit "parts per million" or ppm. It's a way to express a very diluted concentration of one substance mixed in another.

Think of ppm as a ratio: you are comparing the mass of the solute to the mass of the entire solution or a specific part of it.

• 1 ppm is equivalent to 1 gram of solute in 1,000,000 grams of solution.
• Alternatively, it can be seen as 1 mg of solute per liter of water because 1 liter of water weighs about 1,000,000 mg.

This makes ppm incredibly useful for measuring contaminants in water, air, or even food products, where concentrations are typically very low. It allows scientists and engineers to quantify something like the amount of iron in water very precisely.

Mastering the Conversion of Units

Converting units is a critical skill in chemistry, especially when dealing with concentrations. In our example, we began by converting volume from milliliters to liters. This is because the standard unit for expressing ppm is based on mass per volume, with the volume in liters.

• There are 1,000 milliliters in a liter, making conversion straightforward: divide milliliters by 1,000.
• For example, 365 mL converts to 0.365 L with simple division: 365/1000.

Converting units ensures consistency in calculations, and prevents errors that might arise from using mismatched units. It opens the door to accurately determining concentrations, like ppm.

Exploring Solution Concentration

Solution concentration refers to the amount of solute present in a given amount of solvent or solution. It’s crucial for understanding how much of a solute is dissolved in a solution.

In general, concentration can be expressed in several ways:

• Mass per volume (like g/L or ppm)
• Molarity (moles/L)
• Percentage (w/v)

In our scenario, we specifically looked at mass per volume, specifically grams of iron per liter of water. By calculating the mass per volume, and subsequently converting it to ppm, we understood the degree to which iron is concentrated in that solution.

Connecting Mass Per Volume in Calculations

At the heart of concentration calculations is the concept of mass per volume. It's essentially how much of a substance is present in a specific volume of liquid.

Here's how it works in practice:

• First, measure the mass of the solute (in grams).
• Second, measure the volume of the solution (in liters).
• Divide the grams per liter to get a concentration in g/L.

Next, this g/L value is used to easily convert into ppm.
This is vital for practical applications where understanding the precise amount of a substance in a solution is necessary, whether for safety or efficacy reasons. Using mass per volume allows us to express concentrations clearly and allows for conversion to more detailed measures like ppm.